[hinkley]

The problem with factorials is that 20 billion doesn't necessarily mean much.

Let's say we could solve a problem of 100 elements 35 years ago, with 100! operations. If the 2x10^10 multiplier only made the exact same calculation but faster, that would let you solve n = 105 in the same time. Business problems don't grow that slowly. Not over 35 years.

You have to get better at solving the problem in less than n! steps by culling impossible scenarios, and doing it more aggressively.